International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 1, Pages 27-63

Multilocal invariants for the classical groups

Paul F. Dhooghe

Department of Mathematics, Center for Pure and Applied Differential Geometry, KULeuven, Celestijnenlaan 200 B, Leuven 3001, Belgium

Received 11 March 2001

Copyright © 2003 Paul F. Dhooghe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Multilocal higher-order invariants, which are higher-order invariants defined at distinct points of representation space, for the classical groups are derived in a systematic way. The basic invariants for the classical groups are the well-known polynomial or rational invariants as derived from the Capelli identities. Higher-order invariants are then constructed from the former ones by means of total derivatives. At each order, it appears that the invariants obtained in this way do not generate all invariants. The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.